Question

The manager of a high-rise office building plans to display works of art, one per floor, near the elevators. The building has 35 floors. There are 25 sculptures and 18 sketches. What is the probability that the arrangement uses 20 sculptures and 15 sketches?

Answer 1

Step-by-step explanation

We are given the following information:

• The building has 35 floors.

,

• There are 25 sculptures and 18 sketches.

,

• A piece of art is to be displayed per floor.

We are required to determine the probability that an arrangement uses 20 sculptures and 15 sketches.

First, the number of ways of selecting a piece of art per floor is:

`\begin{gathered} ^(43)C_(35) \\ since\text{ }we\text{ }have\text{ }a\text{ }total\text{ }of\text{ }43pieces\text{ }of\text{ }art\text{ }and\text{ }there\text{ }are\text{ }35floors \end{gathered}`

The number of ways of having an arrangement of 20 sculptures and 15 sketches are:

`^(25)C_(20)*^(18)C_(15)`

Therefore, the probability that an arrangement uses 20 sculptures and 15 sketches is:

`(^(25)C_(20)*^(18)C_(15))/(^(43)C_(35))`

Hence, the third option is the correct answer.